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<H2><A NAME="SECTION03742000000000000000"></A>
<A NAME="21113"></A><A NAME="21114"></A>
<BR>
Computational Failures and INFO <B>&gt;</B> 0
</H2>
A positive value of INFO on return from an LAPACK routine indicates a
failure in the course of the algorithm. Common causes are:

<UL><LI>a matrix is singular (to working precision);

<LI>a symmetric matrix is not positive definite;

<LI>an iterative algorithm for computing eigenvalues or eigenvectors
fails to converge in the permitted number of iterations.

</UL>
For example, if SGESVX<A NAME="21117"></A> is called to solve a system of equations 
with a coefficient matrix that is approximately singular,
it may detect exact singularity at the <B><I>i</I><SUP><I>th</I></SUP></B> stage of the <B><I>LU</I></B>
factorization, in which case it returns INFO = <B><I>i</I></B>;
or (more probably) it may compute an estimate of the reciprocal condition number
that is less than machine precision, in which case it returns INFO = <B><I>n</I></B>+1.
Again, the documentation in Part&nbsp;<A HREF="node149.html#partroutines">2</A> should be consulted for a 
description of the error.  

<P>
When a failure with INFO <B>&gt;</B> 0 occurs, control is <EM>always</EM> returned
to the calling program; XERBLA is <EM>not</EM> called, and no error message
is written. 
It is worth repeating that it is good practice always to check for
a non-zero value of INFO on return from an LAPACK routine.

<P>
A failure with INFO <B>&gt;</B> 0 may indicate any of the following:

<P>

<UL><LI>an inappropriate routine was used: 
for example, if a routine fails because a symmetric matrix turns out not to be 
positive definite, consider using a routine for symmetric indefinite matrices.

<P>

<LI>a single precision routine was used when double precision was needed:
for example, if SGESVX<A NAME="21123"></A> reports approximate singularity
(as illustrated above), the corresponding double precision routine DGESVX
may be able to solve the problem (but nevertheless the problem is
ill-conditioned).

<P>

<LI>a programming error occurred in generating the data supplied
to a routine: for example, even though theoretically a matrix should be
well-conditioned and positive-definite, a programming error in generating
the matrix could easily destroy either of those properties.

<P>

<LI>a programming error occurred in calling the routine, of the kind 
listed in Section&nbsp;<A HREF="node135.html#seccommonerrors">7.2</A>.

<P>

</UL>

<P>
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<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
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